Problem: Multiply the following complex numbers, marked as blue dots on the graph: $[3(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))] \cdot [2]$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3(\cos(\frac{4}{3}\pi) + i \sin(\frac{4}{3}\pi))$ ) has angle $\frac{4}{3}\pi$ and radius $3$ The second number ( $2$ ) has angle $0$ and radius $2$ The radius of the result will be $3 \cdot 2$ , which is $6$ The angle of the result is $\frac{4}{3}\pi + 0 = \frac{4}{3}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{4}{3}\pi$.